Aircraft: SMALL TRANSPORT; LOW WING; 2 TURBOJET ENG
Phase of flight: Initial Approach
Anomaly: Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence

I am writing this from a first officer position on a 135 flight. We (referring from here on as crew) departed on schedule for an IFR flight plan route to HOU. Enroute we received instructions from ATC to hold and expect further clearance [in 30 minutes] due to the conditions at HOU. After several minutes we make the decision to divert to our alternate. After descending to begin the arrival for IAH; we get informed by ATC that it has been also shut down. ATC gives us the option to hold; but due to our fuel overhead/situation that was not an option. ATC issued us clearance to 'BPT via direct; descend and maintain 11;000 feet.' At that time ATC said the field was reported VFR and we can get vectored around build ups for a visual or we can shoot the LOC back-course to runway 30. Then they asked us what we would prefer. I had looked up the approaches to runway 30 and noticed and RNAV. After discussing the options; my captain agreed that we should just do the RNAV into RW30. During this time he is hand flying the aircraft with the spoilers extended to get it down faster from altitude. After leveling; I advise him to connect the auto pilot and get no response. Soon after we find ourselves in the clouds getting bumped around as we are being vectored on an extended downwind leg for the approach. I had us set up for the approach with the IAF's all in there and it displayed on the MFD. My captain asks me to get a heading on course back for the approach. I ask ATC and they give me a heading for the base. After asking my captain I request direct to the final approach fix; which is approximately 15 miles out while we are at 3000 MSL. ATC issues 'descend and maintain 2k till established on the approach; cleared RNAV to RW30.' After that I advised my captain to connect the auto pilot to ease the work load; however no response. I changed him up to a NAV needle and armed the approach on the panel for him. At that point we were turning final inside of the final approach fix; so ATC called us and notified us of our deviation and to contact the BPT tower. We should have been at 2000 MSL because we were still outside of the final approach fix and not established; however; we were descending through 2k. I called altitude once; expecting him to make the correction; as I go back heads down on the approach plate. We don't have much time but trying to brief the approach. I remember setting the d(h) and calling out the minimums of the RNAV. I myself was very busy and still have yet to contact the tower. At this point I happened to see that my captain is still descending even though we have not crossed the final approach fix to begin the approach. I then suddenly called altitude then again altitude and the second time very aggressively. During this process I was not getting a response. Then we broke out of the base. I stress to my captain that we are still not on the approach and we should be at 2000k feet. He finally responded and I am going to maintain this. At that point we were at 700-800 feet MSL (and that is verified by flight aware); which was over a 1000k low. When we came out of the bases we were in heavy rain with little visibility. After the fact to find out by the national weather service; the metar was reporting 1.2 SM visibility with 3500RVR at the field. At this point I contacted the tower and we were cleared to land. Just inside of two miles we got the field insight. We were at 800 ft MSL and on the VASI. After the aircraft was on the ground all of this became a discussion. After looking back on the chain of events that lead up to this it is obvious to see some contributing factors. Obviously one major case was the weather but more importantly the aircraft should have been on the auto pilot during this time. It lessens the work load allowing the crew to be more aware of the environment. I was performing all the second in command duties so my captain was just focused on flying the aircraft and wasn't really ready for the approach. We should have taken the time to get everything briefed after I had it set up. I have learned a lot from this event and will not put myself in that situation again. Part 135 First Officer describes a weather diversion into BPT with the Captain becoming fixated and descending well below the published altitude for the approach segment. Attempts by the First Officer to get the Captain back up to the published altitude and to turn on the autopilot are not successful. The 800 foot ceiling allows the approach to be continued to a successful landing.